Joining up to the generalized high degrees

Ellison, P. & Lewis-Pye, A. (2010). Joining up to the generalized high degrees. Proceedings of the American Mathematical Society, 138(8), 2949-2960. https://doi.org/10.1090/S0002-9939-10-10299-8
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We show that every generalized high Turing degree is the join of two minimal degrees, thereby settling a conjecture of Posner's from the 70s.

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